Research on Leibniz at the Hans Kayser Institute for Fundamental Harmonic Research

By Rudolf Haase

Translated by Ariel Godwin

Essay from the Newsletter of the Vienna Academy of Music, 1/1984

The
Author was summoned to Vienna for the purpose of scientific work on
Gottfried Wilhelm von Leibniz (1646-1716). He had already written
articles on Hans Kayser and Johannes Kepler for the encyclopedia Music in History and Present Times (MGG),1
and was considered a specialist in the Pythagorean harmonic tradition,
and was therefore called upon to write an article on Leibniz for the
MGG.2
This was not entirely self-evident, and was actually based only on a
quote from Leibniz that is famous in musicology: “musica est exercitium
arithmeticae occultum nescientis se numerare animi.”3 This sentence, in which the emphasis is on the word unconscious
(directed against the ideas of Descartes), allows for a connection of
Pythagorean and Platonic ideas to an innate musical disposition of the
human soul on the basis of mathematical laws (interval proportions),
and it is likely that Leibniz had further knowledge on music theory.

The intensive study of Leibniz's works and the secondary literature
soon revealed that no one else had tackled this question yet, and
therefore extensive preparatory work was required. As a result, it was
finally concluded that only relatively few statements on music and
music theory existed, in contrast with a multitude of testimonies from
the Pythagorean tradition on the subject of a “universal harmony.” This
led to these ideas being expanded beyond the reference in the MGG
article, and a few essays,4 into a book: Leibniz and Music: A Contribution to the History of Harmonic Symbolism.5

After the calling to Vienna (1965) and the founding of the Institute
(1967), studies on Leibniz were continued; a chapter of the History of Harmonic Pythagoreanism6 was dedicated to Leibniz, and an article was written for Grove's Dictionary of Music and Musicians.7 The results of the studies were finally summarized in a report from the 2nd International Congress on Leibniz, 1972, in Hanover.8

This collection contained two parts. In the first, it was reported that
Leibniz gave many demonstrations for the assumption of a universal
harmony, but that unlike Kepler he did not use interval proportions as
a basis, although Leibniz was familiar with this “universal harmonics.”9
Rather, this idea emerges in a sort of abstract form, transferred from
the realm of natural philosophy to that of metaphysics. In this
interrelation, the concept of harmony plays an important role, standing
right at the center of Leibniz's philosophy, often substituted with
other concepts of similar meaning (parallelism, mirroring, singing in
unison, rhyme, correspondence, chords, sympathy, etc.), and finally
developed to its highest point in the famous concept of prestabilized
harmony,10
that harmony of body and soul determined by God which Leibniz
transferred analogically into other domains and thus built into a
comprehensive metaphysical universal harmony.

The second part of the report describes how Leibniz was also aware of
the study of proportion in music theory, which had already been closely
connected with the concept of universal harmony, so that it was
actually surprising that he did not also apply it together with his
ideas on harmony. In an attempt to answer this question, the hypothesis
was put forward that Leibniz had planned a synthesis of the two
components, but was not able to take them any further; various remarks
(written and oral) shortly before his death can be interpreted to
indicate this.

Studying Leibniz had brought another fact to light, which now had to be
pursued. As was shown in the catalog of Leibniz's letters, published in
1899,11
there was an extensive correspondence with a certain Conrad Henfling,
the content of which dealt exclusively with music theory, but which had
not yet been published. From this it was clear from the outset of the
research that another gap had to be filled, and that all previous
statements on the subject “Leibniz and music” must be incomplete. This
was also discussed at the 2nd
international congress on Leibniz, and the result was that the director
of the Leibniz Archives at the Niedersachsen State Library in Hanover,
where all of Leibniz's legacy is preserved, asked the Author to
undertake the editing of Leibniz's music-related writings, the major
part of which was the correspondence with Henfling. A cursory
examination, along with the assurance of the Leibniz Archive that the
handwriting (very difficult to read) could be sent to Vienna in “plain
text,” led to the acceptance of this task.

Unfortunately, it soon became evident that the promise of delivering
the texts in deciphered form could not be kept (except for one long
letter in Latin from Henfling); but the Author's wife, Ursula Haase,
decided to take on the task of transcribing this correspondence, mostly
in French, from photocopies of the letters. The other assistants of the
Institute, Leopold Spitzer and later Werner Schulze, were also involved
in the difficult and time-consuming editing work, which took many years.

While the transcription progressed slowly, the primary task was the
solution of an important problem, namely that of finding information on
the previously completely unknown Conrad Henfling. This was difficult,
because no reference to him existed in any modern musicological
literature. After a long search, sufficient information on him was
found, and the results published.12 They are briefly summarized here.

Conrad Henfling lived from 1648 to 1716 in Ansbach, and was a court
counselor to the Margrave of Brandenburg-Ansbach, with whose daughter
Caroline he had close contact. In 1705 she became electoral princess of
Hanover (and in 1727, Queen of England). Leibniz lived in Hanover at
the time, and he and Henfling became acquainted through the highly
educated princess, leading to their correspondence between 1705 and
1711. The content of this correspondence relates mainly to music
theory, which Henfling presents in the form of a long letter in Latin
to Leibniz. Henfling's views are very idiosyncratic; this is due not
only to the complexity of his letter, but even more to the
non-pedagogical and sometimes completely incomprehensible nature of his
writing. He asks many questions, and Leibniz finally calls in an
expert, Alphonse des Vignoles, for advice. This leads Henfling to work
towards improvement, and although not all obscurities are resolved,
Leibniz decides to recommend a publication, which actually happens in
1710.13

This publication, as well as Leibniz's patronage, leads one to suppose
that Henfling's name must have been known and preserved for posterity.
But this was not the case. Johann Mattheson does mention him a few
times; but in one of these cases there is a confusion of names, the
background of which is extremely complicated. Finally, a method of
tempering developed by Henfling was attributed to his contemporary in
Ansbach, Georg Heinrich Bümler (1669-1745), and has been handed down
under his name,14 while Henfling was already forgotten by the end of the Baroque period.

Admittedly, clearing up Henfling's identity and his role in the history
of music theory was only a byproduct of the actual work of editing,
which continued gradually and finally led to the publication of the
correspondence.15
The volume contains 27 documents with numerous annotations; an
extensive commentary was also necessary, making up half the length of
the publication, since many problems had to be explained. At the center
is the music theory developed by Henfling, which he explains in the
aforementioned Latin letter. To be precise, the core of the debate is a
new method of tempering.

This method is based on the application of multiple roots, and it
yields an astonishing precision for 10-digit numbers, as is shown by
comparison with the most prevalent temperings of the period. The
calculations only work with the numbers 2, 3, and 5, thus avoiding the
number 7, whose applicability in music theory was widely discussed at
the time (and also in the correspondence). Henfling not only provides
the values for a 12-step tempering, but also develops 19-, 31-, and
50-step subdivisions of the octave with equal precision, compiling them
all in complicated and extensive tables based on the division of a
monochord. Incidentally, in the justification of Henfling's method,
virtually all other tempering methods known at the time (Huygens,
Sauveur, etc.) are discussed. There is a very original further proposal
by Henfling regarding the renaming of the familiar interval terms. He
knew, very correctly, that the traditional theory of steps actually
began with an error in reasoning, namely designating the keynote of a
scale as a “prime” (1st
step), although the sound is not an interval, not a step. Henfling
suggests the term “nulla” instead, and based on this, he develops a
highly different new terminology, which is one of the greatest
complexities of his Latin letter.

The publication of the correspondence between Leibniz and Henfling
finally makes possible the summarization of all aspects of the topic
“Leibniz and music.” It is now clear that Leibniz must have at least
had the knowledge of music theory that he uses in discussion with
Henfling, which we have already summarized. But Leibniz did not get his
knowledge only through Henfling; his answers suggest a considerable
expertise in the field, which he must have acquired earlier and through
which he is entirely on par with Henfling in their discussion. Leibniz
even makes a few hints about this; but sadly, the details of his
studies on music theory are not known-unless there is an as yet
untranscribed remainder of his legacy that will one day give us
information on this. Regardless, we must respectfully conclude that
Leibniz, the great philosopher, mathematician, and universally learned
man, the internationally famous savant of the Baroque period, possessed
knowledge of the highest order in the domain of music theory.